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arXiv · 2509.04287

Simple analyticity criteria for repulsive multi-body potentials

Tyler Helmuth·Marcus Pappik·Will Perkins
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Abstract

We prove a simple, explicit lower bound on the radius of a zero-free disk for Gibbs point processes defined by finite-range, repulsive multi-body interactions. Our lower bound improves on those previously known, and we demonstrate that it is essentially sharp in the generality with which our arguments apply. The key ingredient is a multi-body generalization of integral identities for point densities of Gibbs point processes in the spirit of earlier work of Michelen and Perkins.

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Tyler Helmuth, Marcus Pappik, Will Perkins. 2025-09-04. Simple analyticity criteria for repulsive multi-body potentials. https://arxiv.org/abs/2509.04287

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